Finite Group DatabasebetaFinite Group Databasebeta| order | 980 |
| isoclinism | isoclinic class of D7×D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D35 |
| unambiguous semidirect product | (C5×D7)⋊D7 |
| unambiguous semidirect product | (C7×D7)⋊D5 |
| Fitting, socle, derived, Hall | C5×C72 ⋊ C22 |
| Sylow | C72 ⋊ C2×D5 |
| Sylow | C5 ⋊ D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72 | C22 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 70 |
95 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D72, C2×D7×D35, #64423⋊D5, … |
| maximal normal subgroup of | D5×D72, C2×D7×D35, #64423⋊D5, … |
| maximal quotient of | Dic7×D35, D7×Dic35, #14519977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(980, 27);